Question

question 5
10 pts
g.gsr.6.1 (mc)
find the value of x.
image of a right triangle with a 45-degree angle, hypotenuse 11√2, and one leg labeled x
options:
x = 11
x=5.5
x = √2
x = 5.5√2

Explanation:

Step1: Identify Triangle Type

The triangle is a right - angled isosceles triangle (since one angle is \(45^{\circ}\), the other non - right angle is also \(45^{\circ}\) as the sum of angles in a triangle is \(180^{\circ}\)). In a \(45 - 45-90\) triangle, the legs are equal and the hypotenuse \(h\) is related to the leg \(l\) by the formula \(h = l\sqrt{2}\).

Step2: Apply the Formula

Given the hypotenuse \(h = 11\sqrt{2}\), and using the formula \(h=l\sqrt{2}\), where \(l = x\) (the leg). We can solve for \(x\) by rearranging the formula: \(x=\frac{h}{\sqrt{2}}\). Substitute \(h = 11\sqrt{2}\) into the formula: \(x=\frac{11\sqrt{2}}{\sqrt{2}}\). The \(\sqrt{2}\) terms cancel out, so \(x = 11\).

Answer:

\(x = 11\) (corresponding to the option "x = 11")